*3.2. Heat Transfer Characteristics*

The change in flow characteristics due to the effects of various damage locations on the rotor blade strongly affected the heat transfer on the blade and vane surface. Figure 15 shows the contour distribution of heat flux on the R1 blade surface under various blade conditions. As with the temperature distribution, the heat flux on the suction side was significantly affected, while the effects on the pressure side were negligible. This occurred because of the effects of the blade profile on the flow at the leading edge of the blade. Although the profile became smoother after modification, it considerably altered the flow field, especially at the suction side of the blade. When the profile changed, it generated a stronger vortex and created a larger circulation-flow region on the suction side, as shown in Figure 5a. Therefore, the heat flux on the suction side of the blade increased noticeably when the blade was damaged. Moreover, the heat flux increased significantly at the edges of the damage locations. This caused a sudden increase in thermal stress around the damage locations, which caused the damage to become more critical and reduced the fatigue life of the blade. Another reason for the sudden increase in heat flux around the mid-span was the HS applied to the inlet flow. With the HS, the highest temperature was at the center of the flow. Coupled with the altered blade profile, it caused a significant increase in heat flux at the suction side around the mid-span location. Overall, when the rotor blade was damaged, the heat flux increased suddenly at the suction side of the blade and around the damaged region. Hence, it is necessary to provide a suitable cooling method to prevent excessive thermal stress at these locations.

**Figure 15.** Heat flux distribution on the R1 blade under various blade conditions.

Figure 16 presents the contours of heat flux distribution on the S2 vane surface under various blade conditions. The characteristics of the flow after passing through R1 changed significantly. This considerably affected the heat transfer behaviors on the S2 vane surface on both the pressure and suction sides. On the pressure side, the heat flux increased noticeably when the blades were damaged. The high-heat-flux region extended in the span-wise direction in both the top-damage and middle-damage cases. This phenomenon occurred due to the increased turbulence intensity of the flow and the increased vane surface temperature in the damaged blades. The combined effects of the turbulence intensity and temperature tended to increase the heat flux on the pressure side of the S2 vane. Similarly, the heat flux on the suction side increased due to these coupled effects. The high-heat-flux regions on the pressure side of the vane surface were located around the mid-span, while those on the suction side were located near the hub and tip. Overall, the damaged rotor blade surfaces significantly increased the heat flux on the S2 vane surface. Hence, to protect the vane surface from sudden changes in thermal stress, efficient cooling methods need to be provided at these locations.

**Figure 16.** Heat flux distribution on the S2 vanes surface under various blade conditions.

The tip leakage flow created by the difference in pressure between the pressure and suction sides significantly affected the heat transfer characteristics at the tip surface. To analyze the heat transfer at the blade tip under various blade conditions, contours of the Stanton number distribution on the blade tip were plotted and are shown in Figure 17. The Stanton number can be expressed as follows:

$$St = \frac{q}{(T\_w - T\_0)\rho\_0 V\_0 C\_p} \,\text{}\tag{29}$$

where *q* is the heat flux, *Tw* is the temperature of the wall surface, *T*0 is the average total temperature of the inlet flow, *Cp* is the specific heat of ideal air, and ρ0 and *V*0 are the average density and average velocity of the inlet flow, respectively.

**Figure 17.** Stanton number distribution on blade tip under various blade conditions.

Compared with the reference case, the top-damage cases exhibited lower heat transfer, while the middle-damage cases exhibited higher heat transfer. This result is consistent with the pressure difference and tip leakage flow shown in Figure 10—where the middle-damage cases exhibit more tip leakage flow—as well as with the results of a previous study by Yang and Feng [34]. In addition, the highheat-transfer regions were located on the pressure side of the blade, while the low-heat-transfer regions were located on the suction side. This occurred because the heat transfer at the blade tip was directly

affected by the leakage flow from the pressure side to the suction side of the blade. The tip leakage flow in the top-damage cases was lower than that in the reference case, the high-heat-transfer region near the pressure side narrowed, and the low heat transfer region near the suction side widened. Conversely, the tip leakage flow in the middle-damage cases was higher than that in the reference case, the low-heat-transfer region near the suction side narrowed, and the high-heat-transfer region near the pressure side expanded. Overall, the heat transfer on the blade tip was strongly dependent on the rotor blade conditions. Especially, damage at the middle causes an increase of the heat transfer characteristics, which increased the local thermal stress at the blade tip region.
